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A second order \(\eta \)-approximation method for constrained optimization problems involving second order invex functions. (English) Zbl 1212.90307

Summary: A new approach for obtaining second order sufficient conditions for nonlinear mathematical programming problems which makes use of the second order derivative is presented. In the so-called second order \(\eta \)-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order \(\eta \)-approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear original mathematical programming problem and its associated second order \(\eta \)-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting the original optimization problem.

MSC:

90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming
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References:

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